Elliptic curve isogeny class with Cremona label 78588i (LMFDB label 78588.m)

• Label: 78588i
• Number of curves: $1$
• Conductor: $78588$
• CM: no
• Rank: $0$

Rank

The elliptic curve 78588i1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(37\)	\(1 + T\)
\(59\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 78588i do not have complex multiplication.

Modular form 78588.2.a.i

Elliptic curves in class 78588i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78588.m1	78588i1	\([0, 0, 0, -9, -243]\)	\(-6912/2183\)	\(-25462512\)	\([]\)	\(14592\)	\(0.10024\)	\(\Gamma_0(N)\)-optimal